I dont want to go in to details, where already mentioned head fi org may be a good place to search, but be prepared to read a lot of noncense and hype between as well.
Good advice. I concur, be prepared and bring the hip waders. There are some good folks over there who know what they're talking about, but there is far more noise and B.S. then you'll find here. In general, it is a much younger crowd. That's not always a bad thing at all, but I find there are fewer folks there that I share general musical tastes with, and many seem to be after entirely different qualities from a system than I am. Also there are lots of folks there just entering the hobby who are otherwise easily impressed and have limited experience (not that there isn't that here, but headphones are a far ea$ier entry point so I'd say it is far more prevalent in that world). As anywhere on the Internet, take what you read with a bag of salt.
On closed-back phones; I owned W5000's for a few months and ultimately felt they were quite colored, though I don't think I had an optimal amp for them (the Yamamoto HA02 or ATH's own amp are supposed to match those cans very well).
Notice how many brands of headphones some responders name in their response. If they
were happy with any of them they would likely have stopped searching. Are there better headphones? Probably!
I can only speak for myself - I mention many options because I have experience with many options and I don't believe there is any single solution that will satisfy anyone including STAX. I'm guessing that would be helpful input to the OP as well as knowing that there are many options in that price range that yield very different presentations. I'm not particularly a fan of any of the STAX I've heard, which includes the 02 (best of the bunch that I've heard). They occur to me as too airy and without grounding...lacking a certain tonal density that makes them seem a bit unnatural to my ears. They soundstage like nobody's business so if you like that kind of effect in headphones you'll love Stax (also try HD800, or, sure AKG 1000 if you want to go obscure since they are no longer made which is probably just as much to the point of why they don't last long on the used market as well as being quite unique). I stopped searching at LCD-2's but I do not assume they'd make everyone stop. For me they have a tonal rightness that is utterly effortless and presents the recording as it was laid down. You'd be hard pressed to fault their acoustic presentation, but they are certainly not beyond reproach. I'd say they lag behind many others in soundstaging abilities. They are amazingly detailed cans, like STAX, and yet entirely non-fatiguing. I find LCD-2's very grounded, while STAX are very airy. If you like the out-of-head, speaker-like experience you will not like LCD-2's as the sound pretty much stops at each ear. Some find the out-of-head sounds a bit disorienting and fatiguing in long-term. You should listen for yourself and see if it suits you, but I would advise that taking a short listen vs. sitting down and listening as you might for a few hours will likely be a very different experience. One of the reasons you will find that headphone junkies have tried so many different options is that it's much easier, both financially and physically, to try half a dozen different headphones over time, than it might be to try that many different speakers. I'm not discouraging the previous advice to try STAX - most certainly they are excellent and unique cans - I would temper those posts, once again to point out that you'll find folks who've stopped at all different conclusions as well as those who are not satisfied with any single rig (including STAX). Listen for yourself and find out what works for you. No one here, and no critic that's paid by a magazine, can tell you for certain what you'll enjoy most.